Volume 7, pp. 56-74, 1998.

A block Rayleigh quotient iteration with local quadratic convergence

Jean-Luc Fattebert

Abstract

We present an iterative method, based on a block generalization of the Rayleigh Quotient Iteration method, to search for the $p$ lowest eigenpairs of the generalized matrix eigenvalue problem $Au=\lambda Bu$. We prove its local quadratic convergence when $B^{-1}A$ is symmetric. The benefits of this method are the well-conditioned linear systems produced and the ability to treat multiple or nearly degenerate eigenvalues.

Full Text (PDF) [179 KB], BibTeX

Key words

Subspace iteration, Rayleigh Quotient Iteration, Rayleigh-Ritz procedure.

AMS subject classifications

65F15.

ETNA articles which cite this article

Vol. 31 (2008), pp. 295-305 Hubert Schwetlick and Kathrin Schreiber: A counterexample for characterizing an invariant subspace of a matrix